That's right!
The Amaterasu lineage, despite taking heavy losses during World War 2, managed to largely recover by the era of the three prodigies' birth. Subsequently, another fight came about that drained their power, and just two years later, World War 3 broke out.
Thankfully, the lineages had always maintained a strong control over the government of their territories, with the Amaterasu lineage having a firm grasp of Japan. Each generation of Shogun was one of theirs and subsequently, each Prime Minister had to pay his respects by kneeling in front of the clan head of the Amaterasu lineage.
